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Effects of the WTMASS Parameter in NEiNastran

1. Introduction This example demonstrates the use and effects of the WTMASS parameter in NEiNastran. The model shown in Figure 1 is a 7 in diameter steel plate with a thickness of 0.125 in. The mesh is comprised of 6 elements along the radial and 24 elements around the circumference.

Figure 1. Disk model 2. Model Properties and Conditions The disk is constructed of steel that has a Young’s Modulus (E) of 3.0E7 (psi), and a Poisson’s Ratio (nu) of 0.3. As is common in English units, the Mass Density will be entered as a Weight Density, in this case 0.3 (lbs/in3). The plate property defines a thickness of 0.125 (in). The boundary conditions for this example are a fixed condition around the perimeter of the disk. Constrain all 6 Degrees of Freedom at each node on the disk’s perimeter. 3. Effect on Mass Properties and Gravity Loading First, a load of 1 g in the negative Z-direction is applied to the model. Because the mass density on the material definition was entered in weight units, the gravity load must be applied in factors of g; in this case, the magnitude of the gravity load is 1.

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The total weight of the model can be readily calculated as the volume of the disk times the weight density of the material. The weight of this model is 1.44 lbs. Under a 1 g load, the resultant load vector should be the weight of the model, in this case -1.44 in the Z-direction. NEiNastran reports a total mass in the results summary file of: TOTAL MASS = 1.426740E+00 And a load vector resultant of:

SUBCASE T1 T2 T3 R1 R2 R3

1 0.00000E+00 0.00000E+00 -1.42674E+00 0.00000E+00 0.00000E+00 0.00000E+00 The 0.7% difference from theory is attributed to the discretization of the disk. Adding more elements around the circumference would better approximate the curvature of the perimeter, therefore improving the accuracy of the model. For most all FEA analysis, this error is acceptable. 4. Effect on Normal Modes Analysis The WTMASS parameter plays an important role in performing dynamic analysis. Often, as in this case, the FEA model is built for a stress analysis, and for convenience, weight density is used in place of mass density. This presents a problem when a dynamic analysis is required of the model. Dynamic analysis requires that the density be supplied in mass units. The WTMASS parameter can be specified to convert the global mass matrix from weight to mass units. To convert weight to mass, the weight must be multiplied by a factor of the reciprocal of the gravitational acceleration in the correct units. In our example, the weight density is in lbs/in3. The WTMASS

parameter for this model is: ins

sin

sft in

ftg

2

22

002588.04.3861

121

2.3211

==⎟⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛= .

Table 1 shows a comparison of this model run with the WTMASS parameter correctly specified, as compared to the theoretical natural frequencies of this disk. Table 1. Disk model frequencies

Mode # Theoretical (Hz) NEiNastran (Hz) Error (%) 1 986.3 994.7 -0.852 2050.0 2086.9 -1.8

If the WTMASS parameter is not specified for this model, errors of 95% result. The WTMASS parameter is very important to the accuracy of a dynamic solution when the density has been entered on the material card in weight units. 5. Discussion of NEiNastran vs. MSC.Nastran WTMASS parameters The WTMASS parameter is specified in identical manners in both versions of Nastran. However, the versions differ in how the WTMASS conversion is used. Both versions of Nastran modify the mass matrix with the scalar value specified with the WTMASS parameter. In MSC.Nastran this modified matrix

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is used in the calculations of gravity loads, and generation of mass properties. This results in output that has all been converted to mass units, leaving the user to back out the conversion factor to return to load factors, and model weight. In NEiNastran, this matrix modification is done after the mass properties and gravity loads are calculated. This results in more user friendly output; total mass is reported in the expected weight units.